This is a case where, with rare exceptions, you will have an engine crew (engineer and fireman) who are supplied by the owner/operator of the steam locomotive and are qualified to operate the mechanics of the engine along with a pilot engineer (and, almost certainly, conductor and brakemen) who are supplied by the railroad the excursion is operating over. The pilot will advise the locomotive engineer as to speed restrictions, grade crossing, operating rules and similar while the engineer and fireman tend to the specialties of the steamer. The railroad conductor will manage the overall operation of the train; there will probably be a passenger conductor supplied by the excursion operator to handle the minutia of lifting/validating tickets and dealing with passenger issues.
I would imagine this applies even to (most) Union Pacific steam operations; while it's quite likely that the UP engineers are qualified from Cheyenne to Denver and back (a regular, annual run), when they take one of their steamers farther afield such as to Texas or the West Coast it's statistically highly improbable that the same people are qualified both on a 1940's steam locomotive AND on that particular division of UP territory. So a lucky UP engineer ends up getting a steamer cab ride.